1. Field of the Invention
The present invention relates to a profile measuring method and a profile measuring instrument.
2. Description of Related Art
Some of known profile measuring instruments include a probe that has a stylus tip to be in contact with a workpiece, a movement mechanism for moving the probe, and a controller for controlling the movement mechanism has been conventionally known, where the stylus tip is moved along a target surface of the workpiece while the stylus tip is pressed against the workpiece to measure a profile of the workpiece (see, for instance, Literature 1: JP-A-2005-345123).
A coordinate measuring machine (profile measuring instrument) disclosed in the Literature 1 includes a motion controller that has an autonomous scanning vector generator that generates a velocity vector (probe command value) for moving the stylus tip along a target surface of the workpiece while the stylus tip is pressed against the workpiece.
FIG. 18 shows a stylus tip 100 that is moved along a target surface (lateral face of a truncated cone) of a truncated-cone-shaped workpiece W.
As shown in FIG. 18, the autonomous scanning vector generator defines a workpiece coordinate system for measuring the profile of the workpiece W, in which a central axis of the workpiece W is defined as a ZW-axis, and two axes orthogonal to the ZW-axis are defined as a XW-axis and YW-axis. An instance in which the stylus tip 100 is moved along the measurement target face of the workpiece W within a restraining section S (shown in two-dot chain lines in FIG. 18) of which coordinate value in the ZW-axis direction (i.e. in a height direction of the workpiece W) is set at a constant Zh to measure the profile of the workpiece W at the ZW-axis coordinate value Zh (referred to as a “constant-height scanning measurement” hereinafter) will be described below. It should be noted that a locus LS of a point to be measured (referred to as a measurement target point hereinafter) is represented by a two-dot chain line in FIG. 18. Further, in order to simplify the drawing, a part of reference signs to be used in a later-described formula including the above-mentioned ZW-axis coordinate value Zh is omitted in FIG. 18.
The autonomous scanning vector generator generates a velocity vector VP in an advancement direction of a scanning probe as shown in the following formula (1) supposing that a direction in which the stylus tip 100 is pressed (i.e. a deflection direction of the stylus tip 100) is normal to the measurement target face of the workpiece W at a contact point between the stylus tip 100 and the measurement target face.{right arrow over (V)}P=VS·{right arrow over (P)}u  (1)
In the formula (1), VS is a parameter for controlling velocity in the advancement direction. For instance, the parameter VS is set to be small when a deviation from the target value in the deflection direction or the height direction becomes large.
The vector Pu is a unit vector of a vector P calculated according to the following formula (2).{right arrow over (P)}={right arrow over (E)}×{right arrow over (Z)}u  (2)
In the formula (2), the operator× represents an outer product of the vector, which also applies in the later formulae.
Thus, the vector P is an outer product of a vector E based on a deflection value of the stylus tip 100 and the unit vector Zu in the ZW-axis direction.
The autonomous scanning vector generator also generates a velocity vector VE in the deflection direction as shown in the following formula (3).{right arrow over (V)}E=Ve·(|{right arrow over (E)}|−EO)·{right arrow over (E)}u  (3)
In the formula (3), Ve is a parameter for controlling the velocity in the deflection direction. E0 is a reference deflection value of the scanning probe (i.e. a target value in the deflection direction). The vector Eu is a unit vector of the vector E.
The autonomous scanning vector generator also generates a velocity vector VH in the height direction of the scanning probe as shown in the following formula (4).{right arrow over (V)}H=Vh·(Ch−Zh)·{right arrow over (H)}h  (4)
In the formula (4), Vh is a parameter for controlling the velocity in the height direction. Ch is a ZW-axis coordinate value at a center of the stylus tip 100. Zh is a ZW-axis coordinate value of the restraining section S (a target value in the height direction).
Further, a vector Hh is a vector parallel to the measurement target face of the workpiece W of which magnitude in the ZW-axis direction is 1. The vector Hh is calculated according to the following formulae (5) and (6).
                                          H            →                    h                =                                            H              →                        u                                (                                                            H                  →                                u                            ,                                                Z                  →                                u                                      )                                              (        5        )                                                      H            →                    u                =                                            P              →                        u                    ×                                    E              →                        u                                              (        6        )            
In the formula (5), the operator (,) represents an inner product of the vector, which also applies in the later formulae.
Thus, the vector Hh is equal to the vector Hu divided by the inner product of the vector Hu and the unit vector Zu in the ZW-axis direction. The vector Hu is an outer product of the vector Pu and the vector Eu.
Then, the autonomous scanning vector generator synthesizes each of the velocity vectors VP, VE and VH as shown in the following formula (7) to generate a velocity vector VC (probe command value) in the scanning direction in which the stylus tip 100 is moved along the measurement target face of the workpiece W.{right arrow over (V)}C={right arrow over (V)}F+{right arrow over (V)}E+{right arrow over (V)}H  (7)
FIGS. 19A and 19B illustrate a problem associated with the typical arrangement. Specifically, FIG. 19A is a perspective view of a straight bevel gear W1 (the workpiece). FIG. 19B is a perspective view in which an area Ar1 in FIG. 19A is enlarged to show a tooth flank WF1 (measurement target face).
Incidentally, in order to simplify the drawing, only a part of teeth of the straight bevel gear W1 is shown in solid lines and the rest of the teeth are imaginarily shown in two-dot chain lines in FIG. 19A.
The tooth flank WF1 of the straight bevel gear W1 shown in FIGS. 19A and 19B does not conform to a plane (the above-described restraining section) orthogonal to the ZW-axis (i.e. the central axis of the straight bevel gear W1).
Thus, it is difficult to move the stylus tip along the tooth flank WF1 according to the above-described constant-height scanning measurement and, consequently, it is difficult to measure the tooth flank WF1.
In order to measure the tooth flank WF1 of the straight bevel gear W1 as shown in FIGS. 19A and 19B, a point measurement in which the stylus tip is brought into contact with a plurality of points on the tooth flank WF1 may be employed instead of the autonomous scanning measurement.
However, the measurement of the tooth flank WF1 by way of the point measurement requires much measurement time.